## Kirchhoff pre-stack depth scalar migration
of complete wave field using the prevailing-frequency
approximation of the coupling ray theory

**Vaclav Bucha**
### Abstract

Many ray tracers based on the anisotropic ray theory yield distorted results or
even collapse when shear waves propagating in inhomogeneous weakly anisotropic
models are computed. The coupling ray theory provides more accurate polarizations and
travel times of S-waves in inhomogeneous models with weak anisotropy than the
anisotropic ray theory and solves the problematic behaviour of S-wave polarizations. We
test the application of the prevailing-frequency approximation of the coupling ray theory
to 3D ray-based Kirchhoff pre-stack depth scalar migration and compute migrated
sections in two simple inhomogeneous weakly anisotropic velocity models composed of
two layers separated by a curved interface. The recorded complete seismic wave field is
calculated using the Fourier pseudospectral method. We use a scalar imaging for the
complete wave field in a single-layer velocity model with the same anisotropy as in the
upper layer of the velocity model used to calculate the recorded wave field. We migrate
reflected PP, converted PS1 and PS2 elementary waves without the separation of the
recorded complete wave field. For migration of the S-wave part we use the prevailing-
frequency approximation of the coupling ray theory and for comparison we apply the
anisotropic-ray-theory approximation. Calculations using the prevailing-frequency
approximation of the coupling ray theory are without problems for both models. On the
other hand, for the anisotropic-ray-theory approximation in the model with weaker
anisotropy we have to use limitation of Green function maxima otherwise the migrated
sections are wrong. In spite of complex recorded wave fields, without decomposition, the
migrated interfaces for the vertical component of the PP reflected wave, radial and
transversal components of PS1 and PS2 converted waves are in all stacked migrated
sections relatively good with exception of spurious interface images close to the correct
ones.

### Whole paper

The manuscript is available in
PDF (11570 kB).

Journal of Seismic Exploration, **32** (2023), 105-129.

SW3D
- main page of consortium ** Seismic Waves in Complex 3-D Structures **.